Journal of Applied Probability

Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials

Tuǧrul Dayar and M. Can Orhan

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Abstract

A multiclass c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on drifts. The infinite state space of the model is truncated with an appropriately chosen Lyapunov function. The truncated model is described as a multidimensional Markov chain, and a Kronecker representation of its generator matrix is numerically analyzed.

Article information

Source
J. Appl. Probab. Volume 53, Number 4 (2016), 1098-1110.

Dates
First available in Project Euclid: 7 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1481132839

Mathematical Reviews number (MathSciNet)
MR3581244

Zentralblatt MATH identifier
06675900

Subjects
Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Keywords
Markovian arrival process phase-type service time distribution acyclic phase-type retrial time distribution Kronecker product Markov chain

Citation

Dayar, Tuǧrul; Can Orhan, M. Steady-state analysis of a multiclass MAP/PH/ c queue with acyclic PH retrials. J. Appl. Probab. 53 (2016), no. 4, 1098--1110. https://projecteuclid.org/euclid.jap/1481132839.


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